Assume that \(\mathcal {M}_{f}=\lbrace U\subset M^{\mathbb {N}}~| U~\text{finitely generated}\rbrace \) . From [1]}, \(U_{f}=\bigoplus \lbrace U~|~U\in \mathcal {M}_{f}\rbrace \)  is a generator of \(\sigma [M]\) . Since \(T^{\Lambda }\in \sigma [M]\) , \(T^{\Lambda }\)  is generated by \(U_{f}\) . From [1]}, we have that \(\prod _{\lambda \in \Lambda }^{M}T_{\lambda }=\mathsf {Tr}_{U_{f}}(T^{\Lambda })= T^{\Lambda }\) .
